Symmetrized Block-Product Periodic Marginals in Infinite Translation-Invariant Quantum Chains

Quantum Physics arXiv:2608.10365 (quant-ph) [Submitted on 11 Aug 2026] Title:Symmetrized Block-Product Periodic Marginals in Infinite Translation-Invariant Quantum Chains Authors:Xiao Zeng, Kaiyan Yang, Lingxia Zhang, Zizhu Wang View a PDF of the paper titled Symmetrized Block-Product Periodic Marginals in Infinite Translation-Invariant Quantum Chains, by Xiao Zeng and 2 other authors View PDF HTML (experimental) Abstract:We study local marginals in one-dimensional translation-invariant quantum systems that may hide finite-period structure. Given an $n$-site reduced density matrix, we ask whether it can be obtained by repeating a finite $p$-site block state along the chain and averaging over the $p$ lattice translations. This defines a symmetrized block-product periodic marginal problem, which provides a route both to diagnosing hidden periodic order from local data and to upper bounding ground-state energy densities of infinite translation-invariant local Hamiltonians. We develop two complementary methods. The first is a semidefinite-programming relaxation based on block permutation symmetry and positive partial transpose constraints, which outer-approximates the convex hull of such marginals and yields certified infeasibility tests. The second is a symmetrized matrix product state ansatz, which constructs explicit block-product periodic states and gives variational upper bounds. We benchmark the framework on the Majumdar-Ghosh model, transverse-field Ising, XX, XXZ, and contextuality-related spin models. The results show that the method captures the expected finite-period structure in exactly solvable cases and gives systematically improving variational energies as the period and bond dimension increase. We also formulate a periodic-NPA relaxation for translation-invariant contextuality witnesses and recover the known quantum limits in the tested examples. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2608.10365 [quant-ph] (or arXiv:2608.10365v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.10365 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zizhu Wang [view email] [v1] Tue, 11 Aug 2026 01:45:25 UTC (312 KB) Full-text links: Access Paper: View a PDF of the paper titled Symmetrized Block-Product Periodic Marginals in Infinite Translation-Invariant Quantum Chains, by Xiao Zeng and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 Change to browse by: cond-mat cond-mat.str-el References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)